Kavli Affiliate: Joel E. Moore
| First 5 Authors: , , , ,
| Summary:
Emerging experimental platforms use amorphousness, a constrained form of
disorder, to tailor meta-material properties. We study localization under this
type of disorder in a family of 2D models generalizing recent experiments on
photonic systems. Models in this family reside on amorphous analogs of
kagom’e lattices with fixed coordination number, vary by a tunable synthetic
field, and remarkabaly, permit exact results. We observe two kinds of
localization that emerge in these models: Anderson localization by amorphous
disorder, and the existence of compact, macroscopically degenerate localized
states as in many crystalline flat bands. The flat-band-like degeneracy innate
to kagom’e lattices survives under amorphousness without on-site disorder.
This phenomenon arises from the cooperation between the structure of the
compact localized states and the geometry of the amorphous graph. More
surprisingly, for particular values of the field, such states emerge in the
amorphous system that were not present on the kagom’e lattice in the same
field. Outside the flat band, constrained amorphous graph geometry necessitates
the existence of a fully delocalized state, near which we observe evidence of a
localization-delocalization transition. Our platform serves as a demonstration
of how the qualitative behavior of a disordered system can be tuned at fixed
graph topology and lead to localization phenomena unique to amorphous systems
that are not observed in their generically disordered counterparts.
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